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A286159
Lower triangular region of array A286156, transposed.
3
1, 1, 3, 1, 4, 6, 1, 4, 3, 10, 1, 4, 8, 7, 15, 1, 4, 8, 3, 6, 21, 1, 4, 8, 13, 7, 11, 28, 1, 4, 8, 13, 3, 12, 10, 36, 1, 4, 8, 13, 19, 7, 6, 16, 45, 1, 4, 8, 13, 19, 3, 12, 11, 15, 55, 1, 4, 8, 13, 19, 26, 7, 18, 17, 22, 66, 1, 4, 8, 13, 19, 26, 3, 12, 6, 10, 21, 78, 1, 4, 8, 13, 19, 26, 34, 7, 18, 11, 16, 29, 91, 1, 4, 8, 13, 19, 26, 34, 3, 12, 25, 17, 23, 28, 105
OFFSET
1,3
EXAMPLE
The first ten rows of this triangular array:
1,
1, 3,
1, 4, 6,
1, 4, 3, 10,
1, 4, 8, 7, 15,
1, 4, 8, 3, 6, 21,
1, 4, 8, 13, 7, 11, 28,
1, 4, 8, 13, 3, 12, 10, 36,
1, 4, 8, 13, 19, 7, 6, 16, 45,
1, 4, 8, 13, 19, 3, 12, 11, 15, 55
MATHEMATICA
Map[((#1 + #2)^2 + 3 #1 + #2)/2 & @@ # & /@ Reverse@ # &, Table[Reverse@ QuotientRemainder[n, k], {n, 14}, {k, n}]] // Flatten (* Michael De Vlieger, May 20 2017 *)
PROG
(Scheme) (define (A286159 n) (A286156bi (A002024 n) (A004736 n))) ;; For A286156bi see A286156.
(Python)
def T(a, b): return ((a + b)**2 + 3*a + b)/2
def a(n, k): return T(n%k, int(n/k))
for n in range(1, 21): print [a(n , k) for k in range(1, n + 1)][::-1] # Indranil Ghosh, May 20 2017
CROSSREFS
Transpose: A268158.
Rows converge towards A034856.
Sequence in context: A116416 A051203 A243553 * A307394 A194540 A351153
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 04 2017
STATUS
approved